Finite Group Databasebeta

← #14674134

Subgroups — #14674134

Order 2816.

312 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078995C211yesmaximal, characteristic
2D11×#356C212yesmaximal
3#13066789C211yesmaximal, characteristic, complemented
4#13066788C212yesmaximal, complemented
5C11×#1413C211yesmaximal, characteristic, complemented
6D11×C4⋊Q8C2211yescharacteristic
7#10623219C411yescharacteristic
8C11×#491C2211yescharacteristic
9#10622695C2211yescharacteristic
10#10622682C411yescharacteristic
11#10622415—22no—
12#10622405—22no—
13D11×#101—22no—
14#10622320C411yescharacteristic
15#10622316C411yescharacteristic
16C11×#356C2212yes—
17#10622186C2212yes—
18#10622116—22no—
19C2×Q8×D11D412yes—
20C11×C4⋊Q8C2311yescharacteristic
21C11×#125C2×C411yescharacteristic
22#66997D412yes—
23M16×D11—42no—
24C2×#4313—21no—
25#66949—41no—
26#66945—21no—
27C4⋊C4×D11—41no—
28#66941—21no—
29#66941—41no—
30#66940—41no—
31C42×D11C2×C411yescharacteristic
32#66923C2×C411yescharacteristic
33#66922C2×C411yescharacteristic
34C11×#103—22no—
35C11×#101—22no—
36C11×#97C2×C411yescharacteristic
37#66900—22no—
38#66899—22no—
39#66888—42no—
40#66880—22no—
41C8×Dic11—21no—
42#66874—22no—
43#66867C2×C411yescharacteristic
44#13599—111nomaximal, Sylow
45C2×Q8×C11C2×D412yes—
46Q8×D11—42no—
47Q8×D11—42no—
48C2×C4×D11—21no—
49C2×C4×D11—22no—
50C2×C4×D11C22⋊C411yescharacteristic
51C2×Dic22—22no—
52C2×Dic22—41no—
53C2×Dic22C22⋊C412yes—
54C11×M16—42no—
55C2×C8×C11—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—41no—
58C11×C4⋊C4—41no—
59C42×C11C22×C411yescharacteristic
60(C2×D11)⋊C4—41no—
61C4⋊Dic11—21no—
62C4⋊Dic11—41no—
63Dic11⋊C4—42no—
64Dic11⋊C4—41no—
65Dic11⋊C4—41no—
66C4×Dic11—21no—
67C4×Dic11—41no—
68C4×Dic11C22⋊C411yescharacteristic
69#4318—42no—
70C2×C11⋊C8—21no—
71#4313—42no—
72#4313—82no—
73C8×D11—82no—
74#3139—111no—
75C2×#356—112no—
76#1413—111no—
77#1413—112no—
78#1413D1111yescharacteristic, complemented
79C22×D11#9911yescharacteristic
80Q8×C11—42no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—41no—
84C2×C4×C11C2×C22⋊C411yescharacteristic
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—41no—
88C2×Dic11#9911yescharacteristic
89C4×D11—22no—
90C4×D11—42no—
91C4×D11—42no—
92C4×D11—42no—
93Dic22—42no—
94Dic22—82no—
95Dic22—82no—
96C8×C11—41no—
97C8×C11—82no—
98C11⋊C8—41no—
99C11⋊C8—82no—
100#533—111no—
101C2×C4⋊Q8—111no—
102#491—111no—
103#491—111no—
104#491—111no—
105#491C2×D1111yescharacteristic
106#487—222no—
107#419—222no—
108C2×#101—222no—
109C4×M16—111no—
110#356—112no—
111#356—222no—
112#356C2×D1112yes—
113C22×C11C2×#9911yescharacteristic
114C2×D11—41no—
115C2×D11#35412yes—
116C4×C11—21no—
117C4×C11—41no—
118C4×C11—42no—
119C4×C11—81no—
120Dic11—22no—
121Dic11—21no—
122Dic11—42no—
123Dic11—81no—
124C22×Q8—112no—
125C2×M16—221no—
126C2×M16—442no—
127C4⋊Q8—112no—
128C4⋊Q8—111no—
129C4⋊Q8—221no—
130C4⋊Q8—441no—
131C4⋊Q8C22×D1111yescharacteristic
132#125—111no—
133#125C4×D1111yescharacteristic
134C22⋊Q8—441no—
135C4×Q8—441no—
136#117—221no—
137C2×C4⋊C4—441no—
138C2×C42—111no—
139#103—22no—
140#103—222no—
141#103—222no—
142#103—222no—
143#101—22no—
144#101—222no—
145#101—442no—
146#97—111no—
147#97C4×D1111yescharacteristic
148C4×C8—221no—
149C2×C11—21no—
150C2×C11C2×#35411yescharacteristic
151D11—22no—
152C2×Q8—112no—
153C2×Q8—222no—
154C2×Q8—441no—
155C2×Q8—442no—
156C2×Q8—442no—
157C2×Q8D4×D1112yes—
158C22×C4—111no—
159C22×C4—221no—
160C22×C4—222no—
161M16—42no—
162M16—442no—
163M16—442no—
164M16—882no—
165C2×C8—21no—
166C2×C8—221no—
167C2×C8—882no—
168C4⋊C4—21no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—221no—
172C4⋊C4—442no—
173C4⋊C4—441no—
174C4⋊C4—441no—
175C4⋊C4—441no—
176C22⋊C4—441no—
177C42—111no—
178C42—221no—
179C42—441no—
180C42C2×C4×D1111yescharacteristic
181C11#1359911yescharacteristic, complemented, Sylow
182C23—111no—
183Q8—42no—
184Q8—442no—
185Q8—882no—
186Q8—882no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—111no—
191C2×C4—222no—
192C2×C4—221no—
193C2×C4—222no—
194C2×C4—442no—
195C2×C4—442no—
196C2×C4—442no—
197C2×C4—441no—
198C2×C4C22⋊C4×D1111yescharacteristic
199C8—41no—
200C8—82no—
201C8—441no—
202C8—882no—
203C22—112no—
204C22—441no—
205C22D11×#9911yescharacteristic
206C4—21no—
207C4—41no—
208C4—42no—
209C4—81no—
210C4—222no—
211C4—221no—
212C4—442no—
213C4—881no—
214C2—21no—
215C2—222no—
216C2D11×#35411yescharacteristic
subgroupG/H
centerC2D11×#354
commutatorC42×C11C22×C4
FrattiniC4⋊Q8C22×D11
FittingC11×#1413C2
socleC2×C11C2×#354
prime radicalC22×D11#99
cosocleC11×C4⋊Q8C23
hypercenter#1413D11
hypocenterC11#13599
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1413

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13066789C2semidirect
4. #13066788C2semidirect
5. C11×#1413C2semidirect
78. #1413D11semidirect
181. C11#13599semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130789952
D11×#3562
#130667892
#130667882
C11×#14132
#1359911